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PHYSICS OF THE IMPOSSIBLE
But mathematicians and computer scientists remain undaunted.
To them it is only a matter of time before a thinking machine walks out
of the laboratory.
The most influential person in the field of AI, a visionary who
helped to lay the cornerstone of AI research, was the great British
mathematician Alan Turing.
It was Turing who laid the groundwork of the entire computer revolution. He visualized a machine (since called the Turing machine)
that consisted of just three elements: an input tape, an output tape, and
a central processor (such as a Pentium chip) that could perform a precise set of operations. From this he was able to codify the laws of computing machines and precisely determine their ultimate power and
limitations. Today all digital computers obey the rigorous laws laid
down by Turing. The architecture of the entire digital world owes a
great debt to Turing.
Turing also contributed to the foundation of mathematical logic. In
1931 the Viennese mathematician Kurt Gôdel shocked the world of
mathematics by proving that there are true statements in arithmetic
that can never be proven within the axioms of arithmetic. (For example, the Goldbach conjecture of 1742 [that any even integer greater
than two can be written as the sum of two prime numbers] is still unproven after over two and a half centuries, and may in fact be unprovable.) Gôdel's revelation shattered the two-thousand-year-old dream,
dating back to the Greeks, of proving all true statements in mathematics. Gôdel showed that there will always be true statements in mathematics that are just beyond our reach. Mathematics, far from being the
complete and perfect edifice dreamed of by the Greeks, was shown to
be incomplete.
Turing added to this revolution by showing that it was impossible
to know in general whether a Turing machine would take an infinite
amount of time to perform certain mathematical operations. But if a
computer takes an infinite amount of time to compute something, it
means that whatever you're asking the computer to compute is not
computable. Thus Turing proved that there were true statements in
PHYSICS OF THE IMPOSSIBLE
But mathematicians and computer scientists remain undaunted.
To them it is only a matter of time before a thinking machine walks out
of the laboratory.
The most influential person in the field of AI, a visionary who
helped to lay the cornerstone of AI research, was the great British
mathematician Alan Turing.
It was Turing who laid the groundwork of the entire computer revolution. He visualized a machine (since called the Turing machine)
that consisted of just three elements: an input tape, an output tape, and
a central processor (such as a Pentium chip) that could perform a precise set of operations. From this he was able to codify the laws of computing machines and precisely determine their ultimate power and
limitations. Today all digital computers obey the rigorous laws laid
down by Turing. The architecture of the entire digital world owes a
great debt to Turing.
Turing also contributed to the foundation of mathematical logic. In
1931 the Viennese mathematician Kurt Gôdel shocked the world of
mathematics by proving that there are true statements in arithmetic
that can never be proven within the axioms of arithmetic. (For example, the Goldbach conjecture of 1742 [that any even integer greater
than two can be written as the sum of two prime numbers] is still unproven after over two and a half centuries, and may in fact be unprovable.) Gôdel's revelation shattered the two-thousand-year-old dream,
dating back to the Greeks, of proving all true statements in mathematics. Gôdel showed that there will always be true statements in mathematics that are just beyond our reach. Mathematics, far from being the
complete and perfect edifice dreamed of by the Greeks, was shown to
be incomplete.
Turing added to this revolution by showing that it was impossible
to know in general whether a Turing machine would take an infinite
amount of time to perform certain mathematical operations. But if a
computer takes an infinite amount of time to compute something, it
means that whatever you're asking the computer to compute is not
computable. Thus Turing proved that there were true statements in